Resum:

The present doctoral thesis is to propose the development of mathematical applications in decision-making problems on uncertainty. Applications are focused on relevant aspects of business science in combination of function of the sport in Colombia economic environment in order to identify socio-economic opportunities on sport environment.
Thus, the doctoral thesis focuses on three main items, uncertainty, business opportunities and environment of action. Firstly, the uncertainty generated by environment can be dealt with the mathematics of uncertainty theory applied on business and economics (Gil-Aluja, 1999; Kaufmann and Gil-Aluja, 1986, 1987). Secondly, opportunities depend on characteristics and qualities of the region allowing the development of several economic activities. Economic activity is closely linked to competitiveness, productivity and entrepreneurship; issues that have a particular interest for nations. International and national organizations as World Economic Forum (WEF) and Global Entrepreneur Monitor (GEM) and so on provide reports on current economic stage, business activity and development of the regions in order to make diagnosis and recommendations that a) contribute to growth and economic development and b) promote the creation of new business and employment. Thirdly, sports have been consolidated in the society by the economic power, management and organization that they have achieved (European Commission, 2007).
Based on the above, the research considers to study a) fuzzy set concepts (Zadeh, 1965), principle of gradual simultaneity (Gil-Aluja, 1999, 2000) and OWA operator (Yager, 1988) among others related to the mathematics of uncertainty, b) clusters theory concepts as basis of the competitiveness (Porter, 1998), entrepreneurship from its economic perspective (Audretsch et al., 2002; Stel et al., 2005; Wennekers and Thurik, 1999) and stakeholders from dynamic vision (Fassin, 2009, 2010; Windsor, 2011) as determinants for promoting business activities, c) main characteristics of sports to influence on social and economic spheres simultaneously and Colombia as case of analysis to develop applications in basis of its economic conditions.
Hence, it allows us to make generic developments of the models and mathematical algorithms, which can be used on real cases to observe its usefulness. It has been proposed a new algorithm called fuzzy significance OWA operator (FS-OWA), which is an extension of selection indexes family in OWA operators. This operator allows decisor to take a decision according to the importance he gives the information initially. Likewise, it has been applied several algorithms of existing ones, such as: forgotten effects theory, Moore`s family, Pichat algorithm, Galois lattices, composition max-min, distance indexes, which are very important for developing this doctoral thesis.
Finally, it is important to say that this doctoral thesis makes two significant contributions: applicability and development. On the one hand, applications of models and algorithms are carried out in combination with theorical concepts with real cases showing its usefulness and applicability. On the other hand, a new algorithm is proposed, which aggregates and improves of existing one; this provides a new tool that contributes to the development of the decision theory.
The structure of this doctoral thesis is as follows: In Chapter 1, presentation, justification, aims, methodology, structure and contents are exposed and shown. In Chapter 2, state of question and context of research work are presented. In Chapter 3, mathematical instruments on decision-making are studied focusing on business and economic studies. In Chapter 4, sport and development are studied showing the role of the sport in society as agent of transversal action and the determinants those aid to promote of business opportunities within location. In Chapters 5 and 6, scientific contributions made so far to response to main aim of the research are shown. In Chapter 7, general conclusions, implications and lines of the research are presented. In Chapter 8, bibliography consulted to carry out research work is shown making distinction between scientific articles, books and reports references.